An important issue during the design of an attitude and translational control system for spacecraft is the modulation of commanded control forces and torques towards the thrusters. The design gets even more challenging if additional constraints are taken into account, for instance the requirement that the total mass flow remains constant and that each thruster generates a predefined minimum thrust.
The known modulating algorithm proposed in Hai Ping Jin, Peter Wiktor, and Daniel B Debra's report, “An Optimal Thruster Configuration Design and Evaluation for Quick Step,” 13th IFAC Symposium—Automatic Control in Aerospace—Aerospace Control 1994, Sep. 12–16, 1994 aims to tackle the design issue mentioned above. A principal drawback of this known method, however, is that the constraints cannot be satisfied for high control demands with respect to the ideal maximal thrust which can be generated from the thrusters. The reason for this drawback is that only a small fraction of the thruster null-space is used for the modulation. In contrast, the null space search algorithm of the present invention, as proposed hereinafter, uses the complete null space and therefore higher control demands while satisfying additional constraints can be generated. Another advantage associated with the present invention is that the proposed null space search algorithm is fast and compatible for application to any modulator and therefore can be used to improve any thruster signal proposed by any modulator.